Upper limits for post-wildfire floods and distinction from debris flows

Upper magnitude limits and scaling with basin size for post-wildfire floods are unknown. An envelope curve was estimated defining post-wildfire flood upper limits as a function of basin area. We show the importance of separating peak flows by floods versus debris flows. Post-wildfire flood maxima are a constant 43 m3 s−1 km−2 for basins from 0.01 to 23 to 34 km2 and then declining with added basin area according to a power law relation. Intense rainfall spatial scaling may cause the envelope curve threshold at 23 to 34 km2. Post-wildfire flood maxima are smaller than unburned flood maxima for similar basin area. Rainstorm comparisons indicate that post-wildfire floods are triggered by smaller precipitation depths than unburned floods. Post-wildfire exceptional floods are driven by extreme rainfall rates, in contrast to post-wildfire debris flows. Runoff rates for post-wildfire envelope floods are consistent with infiltration-excess runoff. Future increases in precipitation intensity or wildfire frequency and extent could increase post-wildfire flood upper limits.

The locations of the post-wildfire floods and debris flows analyzed in this work are global in scope but originate primarily from the western United States (Fig. S1).Peak flows from countries outside the United States include locations in Spain, Australia, Israel, Canada, France, South America, South Korea, Greece, and Portugal (Fig. S1).This geographic distribution reflects current data availability and emphasizes the largest magnitude events.In the future, as wildfires affect regions across the globe and post-wildfire peak flows are measured, this database (80) can be updated.

Flow bulking estimation
Peak flows were separated into flow type (i.e., flood, hyperconcentrated flow, debris flow) by the original data sources.To provide an independent assessment of this flow classification, the rational equation was used to estimate flow bulking by converting the unit-area discharge Qu into units of mm hr -1 and comparing to peak rainfall rates.The rational equation for bulking estimation, normalized by A, for the peak observed flow is: where Qu is the unit-area discharge (mm hr -1 ), I is the peak rainfall rate (mm hr -1 ) and C is the runoff coefficient and can be considered the bulking ratio when greater than 1 (19) The peak flow is often attributed to the peak rainfall rate, however a peak flow (especially in the case of debris flows) can be caused by a rainfall rate preceding or succeeding the peak rainfall rate (8).
As an approximation, runoff coefficients and bulking ratios from 0 to 1 can represent floods, from 1-2 represent hyperconcentrated flows, and >2 represent debris flows; bulking ratios for post-wildfire debris flows can be more than 50 times greater than floods (19).Runoff coefficients and bulking ratios can be used as a check for the identification of flow type for measured post-wildfire peak flows, which are typically done by the morphology of flow deposits and visual markers (18).For bulking ratio calculations, peak flows for which there was no information on the time averaging duration of the rainfall rate or the time averaging duration of the rainfall rate was ≥6 hours were excluded from analysis.
The rational method has several key assumptions that can complicate the accuracy of the runoff coefficient estimation and become important limitations on the rational method analysis conducted in this work.Limitations of the rational method include that peak runoff happens at the time of concentration, when the entire watershed acts as the contributing area, which assumes constant and spatially uniform rainfall intensity with a time-averaging duration equivalent to the time of concentration and that the whole watershed contributes to runoff at the outlet.The watershed contributing area may be particularly problematic in basins that <100% burned or burned with a large percentage at low severity.These restrictive assumptions indicate the estimated bulking coefficients in this work should not be taken as precise estimates, but rather as a qualitative indication of whether the original post-wildfire peak flows were correctly classified.
Comparison of bulking ratios (Fig. S2A) suggests that post-wildfire flow types have been correctly characterized based on flow morphology and other indicators of flow type.This indicates that the peak flows can be analyzed as separated flood and debris flow populations based on the original flow classification from the data source.As expected, post-wildfire debris flow bulking ratios are greater than post-wildfire flood bulking ratios (Mann-Whitney U-test pval 8.9e-15).Bulking ratios compared across rainfall rate averaging durations do not indicate a strong dependency of the estimate of bulking ratio on rainfall rate averaging duration for floods from burned basins (Fig. S2B).Peak rainfall rates are not systematically smaller with increasing time interval of averaging for the rainfall rate for post-wildfire floods, with the possible exception of the 60-minute rainfall rates (I-60), shown in Fig. S2C.The I-60 rainfall rates were used for the largest flood basins and the I-30 rainfall rates covered the largest range of basin sizes for post-wildfire floods (Fig. S2D), potentially because the I-30 has been considered a standard intensity for post-wildfire flood characterization and estimation (28).
Comparison of envelope curves for different total burned area fractions in a watershed of 10%, 20%, and 40% and the duration of the post-fire window for peak flows of 5 and 10 years showed minimal sensitivity of the estimated envelope curve to the total burned area fraction and duration of the post-fire window for peak flows between 5-10 years and 10-40% burned (Figure S3).The exponents in the power law ranged from -1.11 to -0.95 between the three percentage-burned and duration criteria of the post-wildfire window for peak flows (Figure S3).
Comparisons to threshold A using envelope curves using different criteria for post-wildfire flood data inclusion of NWIS peak flows indicated the threshold A is most likely between 20 km 2 and 40 km 2 (Fig. S3), which is congruent with the Lanzante procedure estimate.